I know the Gallian book is rife with concrete examples. It certainly can't hurt to be familiar with some of the ideas before you take the class, and that's what I used to investigate before my first class.

I came here to read a cool post, a witty dialogue, a fresh joke, but stumbled upon a "bump"...Way to go, jerk...~CordlessPen

GyRo567 wrote:I know the Gallian book is rife with concrete examples. It certainly can't hurt to be familiar with some of the ideas before you take the class, and that's what I used to investigate before my first class.

GyRo567 wrote:I know the Gallian book is rife with concrete examples. It certainly can't hurt to be familiar with some of the ideas before you take the class, and that's what I used to investigate before my first class.

Don't expect to rely on the solutions manual too much. I mean hopefully you won't go running for it everytime something gets too difficult but also because I don't think it was a very good solution manual. I remember one particular case when I was helping a friend so I thought I'd peak at the solutions because it had been a little while and my hunt went something like... "Gotta find Exercise 4.17... Ok under 4.17 it says see 4.32... where it further sends me to an example in the book... where they refer me to Exercise 4.17... (sigh)"

GyRo567 wrote:I know the Gallian book is rife with concrete examples. It certainly can't hurt to be familiar with some of the ideas before you take the class, and that's what I used to investigate before my first class.

Don't expect to rely on the solutions manual too much. I mean hopefully you won't go running for it everytime something gets too difficult but also because I don't think it was a very good solution manual. I remember one particular case when I was helping a friend so I thought I'd peak at the solutions because it had been a little while and my hunt went something like... "Gotta find Exercise 4.17... Ok under 4.17 it says see 4.32... where it further sends me to an example in the book... where they refer me to Exercise 4.17... (sigh)"

I won't run to it every time something seems just above my abilities (if I don't push myself, I won't get any better at math). I'll reference it when I either have no idea what to do or I work on something for hours, always get to the same (wrong) answer, or to check answers after I've solved a problem.

If you enjoy mathematics from an abstract perspective I would recommend Herstein's Abstract Algebra. The book is somewhat self contained (i.e. a thorough intro chapter to the basics) and has exercises at a few levels of difficulty. The book also provides a nice foundation for graduate books like Herstein's Topics in Algebra or Hungerfords Algebra.

On the other side the book doesn't stray far from abstract algebra and you won't find the same extras as in Gallian's Contemporary Abstract Algebra. These extras include biographical information on mathematicians who shaped abstract algebra, computer related assignments, and papers for further reading on certain topics.

romulox wrote:On the other side the book doesn't stray far from abstract algebra and you won't find the same extras as in Gallian's Contemporary Abstract Algebra. These extras include biographical information on mathematicians who shaped abstract algebra, computer related assignments, and papers for further reading on certain topics.

I really liked the short biographical information sections in Gallian's book. We never had to do any of the computer related assignments (but I wish we would have).

If you enjoy mathematics from an abstract perspective I would recommend Herstein's Abstract Algebra. The book is somewhat self contained (i.e. a thorough intro chapter to the basics) and has exercises at a few levels of difficulty. The book also provides a nice foundation for graduate books like Herstein's Topics in Algebra or Hungerfords Algebra.

On the other side the book doesn't stray far from abstract algebra and you won't find the same extras as in Gallian's Contemporary Abstract Algebra. These extras include biographical information on mathematicians who shaped abstract algebra, computer related assignments, and papers for further reading on certain topics.

Hope this helps.

-romulox

I have been moving recently so I hope this reply isn't too late.

You're not too late so you have nothing to worry about, especially because Herstein's book is much cheaper which allows me to justify having two Abstract Algebra books than if it was the same price as Gallian's Contemporary Abstract Algebra. Also, since I've heard that Abstract Algebra is quite difficult, it couldn't hurt to have a second book for reference. Thank you for your recommendation.

Hi I was introduced to Calculus via my AP Calculus BC class this year and I was hoping to go back and maybe get a more rigorous foundation before I go into my Honors Cal III course this fall. I was wondering what book would be best. Spivak seems to come with very high recommendation. I'd also look well on a book that has a good section on Polars, I'm kind of lacking in knowledge of how to work with them.

Durin wrote:Hi I was introduced to Calculus via my AP Calculus BC class this year and I was hoping to go back and maybe get a more rigorous foundation before I go into my Honors Cal III course this fall. I was wondering what book would be best. Spivak seems to come with very high recommendation. I'd also look well on a book that has a good section on Polars, I'm kind of lacking in knowledge of how to work with them.

I used this book for my calculus 1 class and used it as a reference for my calculus 2 and 3 class. I just looked through it and it contains all of the polar stuff you'll need. http://www.amazon.com/Calculus-Early-Tr ... 882&sr=8-1 It is written very clearly and has many examples, it's one of the only mathematics books that I've ever been able to use to teach myself easily. It also spans calculus 1, 2, and 3 so you can use it as a reference for just about any calculus class. Unfortunately, I've never used Spivak so I have no input with regards to that.

Dover is a great first place to look. I have heard good things about Lovelock, and they have also reprinted one by Henri Cartan, who cannot possibly steer you wrong. I haven't used either of them myself. I got most of my forms via Loring Tu's Introduction to Manifolds (who also did Differential Forms in Algebraic Topology, a course I took from him but admittedly understood ~5% of what went on) and from Spivak, esp vol 2. I am told that differential forms are also useful in flat space, which is probably more what Lovelock and others are doing. Do Carmo also has a book on it, Amazon tells me, and while I haven't read it or heard much about it, I have infinite love for his curves and surfaces book, so I don't hesitate to recommend his others.

LE4dGOLEM: What's a Doug?Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

For graphing, beginner to intermediate, check out the algebra 1 and 2 books as they are meant for schools and do an awesome job of explaining how stuff works. You actually don't even have to buy it just go to hotmath.com and look at the various types of books they have with problems worked out even.

Keisler's "Elementary Calculus - An Infinitesmal Approach" is freely available on the Internet; depending on the way you think, you may get better mileage (more intuitive explanations) out of this book than other calculus textbooks. (AussieSwede, try reading this.)

Looking through my other collected maths notes, Nearing (of UMiami) and Michael D. Alder have produced some truly excellent notes which are available as free PDFs.

For dead-tree books, Blinder's "Guide To Essential Math" is superb for a refresher on everything up to about 2nd/3rd year undergrad maths; Kreyszig and Stroud are also good.

Does anybody have reccomendations for good books on introductory discrete mathematics? I cna pretty much do anything that I need to algebraically, but I don't know calculus so any book with a heavy focus on it is useless to me.

kenneth rosen's discrete mathematics and its application is pretty good. it covers most major and minor areas in discrete mathematics though you may have to find a good supplement for a sound treatment of first order logic and boolean algebra. The book does not cover most topics in any sort of depth and really is an undergraduate level introduction book.

for the future (or if you find rosen's book lacking depth) i would recommend tarski's intro to logic. this will give you a bit more on the logic side.

for combinatorics brualdi's book is pretty good (we used the 4th edition) and is probably considered graduate level.

for graph theory west's book is good. it is graduate level and difficult to get through without some sort of help (i.e. a professor)

many intro discrete math books also cover searching and sometimes computer science topics such as data structures or coding theory. you will have to find separate in depth books for these topics.

Can anyone recommend a good book or two on set theory and the foundations of mathematics for self-study? I don't have an extensive background in math or logic (I've taken linear algebra, diff. eq., and a couple of math methods for physicists classes, and a basic logic class that went as far as Peano arithmetic), so I'll need it to be somewhat pedantic, but I'd like something that's fairly rigorous. Preferably something that covers ZFC but also touches on other systems and discusses Godel's incompleteness theorems.

I am looking for some refresher books as i have been out of secondary school for over 10 years, I am mainly looking for books that i could teach myself from high school to advanced level (preferably in the same book). I am looking for many subjects including: analytical statistics (especially if it covers risk management and process control formulae), Trigonometry (mainly looking for good resources for functions, identities, and algebraic geometry), a good resource for beginning to mid level algebra, a good resource for beginning to mid level calculus, and a good resource for beginning to mid level physics. I know that this will be a pretty long list but I really just want to get reacquainted with actually knowing how to do math without always having to use a calculator. I do remember many of the principles, and I do use them quite often but I would like to brush up my math skills before I try to go back to university.

romulox wrote:kenneth rosen's discrete mathematics and its application is pretty good. it covers most major and minor areas in discrete mathematics though you may have to find a good supplement for a sound treatment of first order logic and boolean algebra. The book does not cover most topics in any sort of depth and really is an undergraduate level introduction book.

for the future (or if you find rosen's book lacking depth) i would recommend tarski's intro to logic. this will give you a bit more on the logic side.

Currently, the book I have is Johnsonbaugh because it's the only book my high school math department had (this beggar was not a chooser). I have managed to learn things from the book, but it can be confusing at times. Is it really worth paying for Rosen, waiting for it to arrive, try to figure out where I am in that book etc. etc. instead of just continuing on? Is it really that much better?

grimreeker, i have not personally used Johnsonbaugh's book. i read a few amazon reviews which seemed to imply the book was not very good.

sometimes you can find older editions of good books for cheaper.

i am not saying rosen's book is the best, only that i have used it and that it is sufficient, broad, and mostly coherent. many times a place where a book falls short is where a professor will step in. books very often fall short which is one of the reasons self study for sufficiently non-advanced students can be difficult.

practically though sometimes you have to use what you can get and ask the fora for help.

I found Lang's Undergraduate Linear Algebra to be quite awesome. (and not at all like his algebraic number theory book which is horrifyingly harsh)It was an old copy my dad gave to me, and as such the answer keys had a lot of mistakes (not a very revised edition).That wasn't a big problem for me because I had another book filled with linear algebra questions to solve, and used Lang mainly for rigorous proofs that the class book furiously hand-waived away.If you want to work through a bunch of problems there's also Zhang's Linear Algebra: basically a small book filled with problems of varying difficulties. Quite fun imo, should complement Lang pretty well.

Godement's "Cours d'Algèbre" is a thing of sheer beauty. If you can read French/get a translated copy, that will DEFINITELY be worth it. It is extremely rigorous, starts off with some axiomatic set theory and then proceeds onwards, mixing through topics in linear algebra, groups, rings, and fields, and number theory. It all fits in very smoothly, and the exercises are REALLY worth your time. He'll walk you through difficult proofs (sometimes making you prove the same result in different ways) and really get you used to the concepts without hammering it into you the way a, say, undergrad university book would do. What I'm trying to say is that it's not repetitive busy-work but filled with meaningful exercises; you won't get that "well that was totally contrived" feeling working on his.

Other than that... Well there's always Mathematics: It's Content, Methods, and Meaning, by Aleksandrov, Kolmogorov,and Lavrent'ev. If you look at the old "book club" thread, you'll get a detailed idea of what to expect from that book. That's the book that got me into math in the first place, and it covers a huge range of topics with great depth.

Yakk wrote:hey look, the algorithm is a FSM. Thus, by his noodly appendage, QED

I am looking for a proof-based high school geometry book. I love the Geometry for Fun and Challenge by Dolciani, but have not found one that matches up to what I refer to as Little Red, the 1990's edition. Today's texts are too testing oriented. Would love to find one, especially a paper back for affordability for classroom use. Thanks

This was an INTRODUCTORY algebra course, in case you only took pre-algebra in high school. That happens a lot here. The book assigned, however, basically goes "Blah blah math you can create a line with 2 points in a graph like y = mx + b where ... oh hell, math sucks, look here's how to do it with a calculator!" It taught more the use of a calculator than the subject of algebra.

So now I've been peeking at other textbooks. I bought a few older ones for $5 each ... one is supposed to be good; the other, however, introduces Algebra with Geometry.

Yes, I said that.

It introduces algebra with geometry.

Instead of handing you algebra (vaguely) and then a calculator, like the s#!t they assigned in class, it fully explains algebra concepts and then moves into geometry that you can handle with your limited understanding of algebra. At least that's what it says in the description.

In any case I like the idea of teaching math with more math. It seems more leisurely. You're learning an application of a concept, rather than being told to memorize a raw concept and practice with example problems by rote and boredom. This is like taking a physics class and building catapults instead of doing equations about the tension of a hanging weight.

Any thoughts on a decent, cheap math text or supplemental math material? I've got the Master Math series, a few algebra texts, and I'm working on learning a Japanese Soroban (and writing an introductory text focused on that); but better guidance is always better. I'm teaching myself, since college is bad at this.

I'm looking for books on Combinatorics, Graph Theory and Discrete Math. I'm in my last year of high school, so ideally I'd like a book that covers the basics, but still manages to cover the more interesting topics. I've taught myself how to program and am currently making my way through Skienna's [url=http://www.amazon.com/Algorithm-Design-Manual-Steven-Skiena/dp/1848000693]The Algorithm Design Manual[url], so I've got a basic understanding of graph theory and combinatorics but I really do mean basic.

"Pearls in Graph Theory" is a very good book on the subject, based on previous posts buried deep in the thread. I own the book, but have only given it a cursory glance, so I don't know how easy or hard it is.(I also don't know about the other two mentioned)

Yakk wrote:hey look, the algorithm is a FSM. Thus, by his noodly appendage, QED

I'm starting to become interested in functional analysis, now I know that it would be incredibly difficult to self study it, especially because I have no background in analysis. So are there any recommendations for introductory analysis texts that would provide a decent background in analysis that would make taking a stab at functional analysis not an incredibly brutal task? Since it's most likely relevant, here's my math background. Calculus 3, linear algebra, currently taking differential equations, and currently - basically guided self-studying abstract algebra.

Introduction to Analysis by Maxwell Rosenlicht is a cheap little Dover book, and it has more explanatory power than baby Rudin. Or you could just try to work through the two Rudin books. (Or Royden for Lebesgue integration/measure theory)

I came here to read a cool post, a witty dialogue, a fresh joke, but stumbled upon a "bump"...Way to go, jerk...~CordlessPen

I like the subject calculus when I was taking Electronics Engineering. We used Differential and Integral Calculus by Ph.D Clyde E. Love and Ph.D. Earl D. Rainville. The explanation, illustrations and examples are clear and easily understood.

I'm hoping to enroll into a four-year college next fall with the intention of pursuing a mathmatics major. I have always loved mathematics, and when in high school the books I would typically read would be mathematics books and computer science books.

In the mean time, I'm wondering if anyone has any books they would recommend I read (or puzzle books that would be fun to work through). I currently have an Amazon Wish List set up with some mathematics books listed in there. If there is a book you would suggest that is already on my Wish List, please let me know, so I know I've picked a winner and I know what to look for first.

Some mathematics texts I have already read (and remember) include Euclid's Window and Mathematics: From the Birth of Numbers, but it's been a while.

My Amazon Wish List is located here: http://amzn.com/w/1VN169EZ658KL

I would greatly appreciate any suggestions and comments! (I would also appreciate any films that deal with math heavily [whether fiction or non-fiction, these can be just for fun], such as A Beautiful Mind and Pi)

Trask Fujioka wrote:I'm hoping to enroll into a four-year college next fall with the intention of pursuing a mathmatics major. I have always loved mathematics, and when in high school the books I would typically read would be mathematics books and computer science books.

In the mean time, I'm wondering if anyone has any books they would recommend I read (or puzzle books that would be fun to work through). I currently have an Amazon Wish List set up with some mathematics books listed in there. If there is a book you would suggest that is already on my Wish List, please let me know, so I know I've picked a winner and I know what to look for first.

Some mathematics texts I have already read (and remember) include Euclid's Window and Mathematics: From the Birth of Numbers, but it's been a while.

I would greatly appreciate any suggestions and comments! (I would also appreciate any films that deal with math heavily [whether fiction or non-fiction, these can be just for fun], such as A Beautiful Mind and Pi)

GEB is interesting but long, you could spend a lot of time reading that when you could be reading other things. On the other hand, it's a great introduction to formal logic which is something you'll be studying.

At your age I also enjoyed Chaos by James Gleick, although it spends a bit too long trying to be atmospheric without explaining the math, and Uncle Petros and Goldbach's Conjecture by Apostolos Doxiadis, which is a novel.

Recently I enjoyed How the Universe Got Its Spots by Janna Levin, which I actually picked up at the NASA gift shop in Houston. I was reading it as a math graduate, but it seemed accessible.

I'm looking for a book (Or resource) that will cover the "foundation of math." Topics that I think will fall under this, are set theory, basic (BASIC- Like, 2 comes after 1) number theory, arithmetic, and maybe some basic algebra and geometry.

The book doesn't necessarily have to be for "beginners", actually, I would prefer it to be aimed at higher mathematicians as long as it is still covering the foundations. I found Basic Math and Pre-algebra for Dummies and it fits rather well. However, I am of the school of thought that multiple, different, and independent sources are the only way to truly learn.

Lastly, the reason I am looking for books like this is to restore my horrible foundation in mathematics. I want to know WHY this works, not just memorize a solution and repeat it whenever I identify the situation.

One of my professors talked about a class that he took in grad school called "Foundations of algebra" and it seems like his class covered exactly what you are describing. However, he was just handed a 20 page packet and was told to finish it by the end of the semester so I can't really give a book recommendation, but maybe you can look for books using those keywords that aren't for 7th-9th graders.

I was hoping someone could suggest a good basic book on proof writing (or at least that includes it). I'm starting abstract algebra next semester, and I haven't done any proof based classes before, so I'd like to get a feel for it before I start the class.